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# LowTFMuonium¶

## Description¶

A relaxation function for a pair of transver field triplet muonium frequencies.

$A(t)=\frac{A_0}{4}\{(1+\delta)a_{12}\cos(\omega_{12}+\phi)+ (1-\delta)a_{23}\cos(\omega_{23}+\phi)\}$

and,

$\delta= \frac{\chi}{\sqrt{1+\chi^2}},$
$\chi = (g_\mu+g_e)\frac{B}{A},$
$d = \frac{(g_e-g_\mu)}{g_e+g_\mu},$
$E_1=\frac{A}{4}(1+2d\chi),$
$E_2=\frac{A}{4}(-1+2\sqrt{1+\chi^2}),$
$E_3=\frac{A}{4}(1-2d\chi),$
$\omega_{ij}= 2 \pi (E_i - E_j),$
$a_{ij}=\frac{1}{(1+(\omega_{ij}/(2\pi f_\text{cut}))^2)},$

where,

$$A_0$$ is the amplitude,

A (MHz) is the isotropic hyperfine coupling constant,

$$\phi$$ (rad) is the phase at time $$t=0$$,

$$g_\mu = 0.01355342$$ , the gyromagnetic ratio of muon,

$$g_e = 2.8024$$ , the gyromagnetic ratio of electron,

and $$f_\text{cut} = 10^{32}$$ (MHz).

## Properties (fitting parameters)¶

Name

Default

Description

A0

0.2

Amplitude

Field

0.1

Magnetic Field (G)

A

0.2

Isotropic hyperfine coupling constant (MHz)

Phi

0.0